Mastering Special Right Triangles: 45-45-90 and 30-60-90 Explained

Learn how to solve special right triangles: 45-45-90 and 30-60-90. Discover their unique ratios for finding missing sides.

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Special right triangles, such as 45-45-90 and 30-60-90 triangles, have set ratios. For a 45-45-90 triangle, the legs are equal, and the hypotenuse is the leg length multiplied by √2. For a 30-60-90 triangle, the shortest side is opposite the 30° angle, the hypotenuse is double that side, and the longer leg (opposite the 60° angle) is the short side multiplied by √3. Use these ratios to quickly solve for missing sides.

FAQs & Answers

  1. What are the ratios for a 45-45-90 triangle? In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is the leg length multiplied by √2.
  2. How do you solve a 30-60-90 triangle? In a 30-60-90 triangle, the shortest side is opposite the 30° angle, the hypotenuse is double that side, and the longer leg is the short side multiplied by √3.

Watch More

If you found this video on special right triangles helpful, check out our other videos on geometry concepts and math problem-solving techniques to further enhance your understanding.

  1. Understanding the 30-60-90 Triangle Rule: Essential Geometry Tips Explore the unique side ratios of 30-60-90 triangles and simplify your geometric calculations with this quick guide.
  2. Understanding the 45-45-90 Triangle Formula Discover the formula for a 45-45-90 triangle and learn how to calculate its sides effectively.
  3. Calculating the Hypotenuse of a 45-45-90 Triangle: A Step-by-Step Guide Learn how to easily find the hypotenuse of a 45-45-90 triangle with our quick and clear guide.